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A runs test for stock-market prices with an unobserved trend

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  • Herger, Nils

Abstract

To test whether stock-market prices follow a random walk, the algebraic signs of their returns have been analyzed like a sequence of coin tosses. Similar to coin tosses, which represent Bernoulli trials with equiprobable outcomes, signed returns lend themselves for a simple runs test for randomness. However, stock-market prices typically comprise an unobserved trend implying that even under pure randomness positive and negative returns are not necessarily equally probable. Therefore, it is difficult to infer the behavior of stock-market prices from the traditional runs test. Fortunately, the von Neumann algorithm allows to transform tosses of a potentially unfair coin, meaning that it could suffer from an unknown bias, into equiprobable outcomes. This is done by tossing the coin twice and retaining only the first observation when different outcomes arise. Applying the same “trick” to pairs across a sequence of signed stock-market returns paves the way for a runs test that is robust to the effects of constant, unobserved trends.

Suggested Citation

  • Herger, Nils, 2025. "A runs test for stock-market prices with an unobserved trend," The North American Journal of Economics and Finance, Elsevier, vol. 80(C).
    • Handle: RePEc:eee:ecofin:v:80:y:2025:i:c:s1062940825001093
    DOI: 10.1016/j.najef.2025.102469
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    References listed on IDEAS

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    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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